Oxygen transfer in a convection-enhanced hollow fiber bioartificial liver.

A mathematical model was developed to predict oxygen transport in a hollow fiber bioartificial liver device. The model parameters were taken from the HepatAssist 2000 device, a plasma perfused hollow fiber cartridge with primary hepatocytes seeded in the extracapillary space. Cellular oxygen uptake was based on Michaelis-Menten kinetics. Oxygen transport due to the convective flow of plasma into the extracapillary space was considered. The effect of modulating several important parameters was investigated, namely, the Michaelis-Menten constant V(m) (the maximum oxygen consumption per unit volume of the cell mass), the oxygen partial pressure, the flow rate of the plasma at device inlet, and the permeability of the cell mass contained in the extracapillary space. A computer implementation of the model was used to assess whether a given number of cells could be maintained within such a device. The results suggest that a substantial proportion of the hepatocytes are exposed to hypoxic conditions under which metabolism may be impaired.

Self-organization, scale and stability in a spatial predator-prey interaction.

Simple predator-prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig-McArthur model with immobile prey can be stabilized by self-organized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the self-organized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic.

Oxygen transfer in a diffusion-limited hollow fiber bioartificial liver.

A mathematical model was developed to predict oxygen transport in a hollow fiber bioartificial liver device. Model parameters were taken from the Hepatix ELAD configuration; a blood perfused hollow fiber cartridge with hepatocytes seeded in the extracapillary space. Cellular oxygen uptake is based on Michaelis-Menten kinetics, and nonlinear oxygen transport in the blood is considered. The effect of modulating three important parameters is investigated, namely, the Michaelis-Menten constants Vm (volumetric oxygen consumption of the hepatocytes) and Km (half-saturation constant), and hollow fiber oxygen permeability. A computer implementation of the model is used to assess whether a given cell mass could be maintained within such a device. The results suggest that liver cell lines possessing low rates of oxygen consumption could be maintained if membranes of sufficiently high oxygen permeability are used. For primary hepatocytes, which have much higher oxygen demands, radial transport of oxygen is rate limiting, and the axial-flow hollow fiber cartridge is thus an inappropriate design for use as a bioartificial liver with primary hepatocytes.

The characteristics of epidemics and invasions with thresholds.

In this paper we report the development of a highly efficient numerical method for determining the principal characteristics (velocity, leading edge width, and peak height) of spatial invasions or epidemics described by deterministic one-dimensiohal reaction-diffusion models whose dynamics include a threshold or Allee effect. We prove that this methodology produces the correct results for single-component models which are generalizations of the Fisher model, and then demonstrate by numerical experimentation that analogous methods work for a wide class of epidemic and invasion models including the S-I and S-E-I epidemic models and the Rosenzweig-McArthur predator-prey model. As examplary application of this approach we consider the atto-fox effect in the classic reaction-diffusion model of rabies in the European fox population and show that the appropriate threshold for this model is within an order of magnitude of the peak disease incidence and thus has potentially significant effects on epidemic properties. We then make a careful re-parameterisation of the model and show that the velocities calculated with realistic thresholds differ surprisingly little from those calculated from threshold-free models. We conclude that an appropriately thresholded reaction-diffusion model provides a robust representation of the initial epidemic wave and thus provides a sound basis on which to begin a properly mechanistic modelling enterprise aimed at understanding the long-term persistence of the disease.

Optical modelling of light distributions in skin tissue following laser irradiation.

A Monte-Carlo method is used to compute light distributions in a multilayer skin model for variable width finite beams. By means of a 4-layer skin model in which blood may be represented as a discrete layer, vascular lesions such as port wine stains may be studied. Light distributions and thermal profiles are simulated, representing the irradiation of a port wine stain using 577 nm and 585 nm wavelengths. Damage thresholds at 585 nm are found to substantially exceed those predicted at 577 nm, although the nature of the damage differs at the two wavelengths. Variations due to beam width are found to be unimportant if the diameter exceeds 1 mm. The predictions are compared with clinical results, and a novel 5-layer approach based on new optical parameters is adopted to account for discrepancies in epidermal temperature.

Optimum laser parameters for port-wine stain treatment.

The choice of suitable laser parameters is important for effective treatment of port-wine stains. The considerations in the choice of laser parameters are discussed with the aim of coagulating and sealing the abnormal blood vessels and completely denaturing the associated perivascular tissues, while confining the thermal damage to the vicinity of the abnormal vessels. A mathematical model was used to simulate the volume absorbed photon intensity in skin for argon, dye, Nd:YAG, and CO 2 lasers. The model computes the number of photons absorbed within each region, and an optimum wavelength is chosen by selecting that which has the highest absorption ratio in the blood vessel compared with absorption in the epidermis and dermis. The model further computes the input energy and the corresponding pulse duration required to seal the blood vessels and hence remove the port-wine stain.